In the following questions , there are statements followed by conclusions . Choose the conclusions which must logically follow from the given statements .
Statements :
1. Some candidates are students .
2. All children are citizens
3. All citizens are candidates
Conclusions :
I. Some citizens are students
II. Some candidates are children
III. All children are candidates
IV. No child is student

Options

A. Only I and II
B. Only II and III
C. Only III and IV
D. Only I, II and III

Answer

To solve the given problem, we need to analyze the statements and conclusions logically. Let's break it down step by step.

### Step 1: Analyze the Statements
1. **Some candidates are students.**
- This means there is an intersection between the set of candidates and the set of students.

2. **All children are citizens.**
- This means the set of children is completely contained within the set of citizens.

3. **All citizens are candidates.**
- This means the set of citizens is completely contained within the set of candidates.

### Step 2: Draw the Venn Diagram
- Draw three circles: one for candidates, one for students, and one for citizens.
- The circle for citizens should be inside the circle for candidates, since all citizens are candidates.
- The circle for children should also be inside the circle for citizens, since all children are citizens.
- The intersection of candidates and students should be marked to show that some candidates are students.

### Step 3: Evaluate the Conclusions
Now, let's evaluate each conclusion based on the Venn diagram:

1. **Conclusion I: Some citizens are students.**
- This conclusion cannot be definitively drawn because there is no necessary overlap between citizens and students based on the statements. Therefore, this conclusion is **not valid**.

2. **Conclusion II: Some candidates are children.**
- Since all citizens (which include children) are candidates, and some candidates can overlap with children, this conclusion is **valid**.

3. **Conclusion III: All children are candidates.**
- Since all children are citizens and all citizens are candidates, it follows that all children are indeed candidates. Therefore, this conclusion is **valid**.

4. **Conclusion IV: No child is a student.**
- This conclusion cannot be definitively drawn because while it is possible that no child is a student, it is also possible that some children could be students. Therefore, this conclusion is **not valid**.

### Final Answer
Based on the evaluation:
- Valid conclusions are **II and III**.